Ideal Liquid Compression Refrigeration Cycle

ABSTRACT

Liquid compression refrigeration cycle (LCRC) is a new cycle, that can be applied in the refrigeration and heat pump applications, this cycle has achieved the coefficient of performance of the reversed Carnot cycle, unlike the vapor compression cycle, where a clear deviation from the reversed Carnot cycle is appeared in it&#39;s ideal case, these deviations from the reversed Carnot cycle have been solved in the Liquid Compression Cycle (LCRC) to achieve a thermal efficiency more than the Vapor Compression Cycle (VCRC) efficiency.

FIELD OF THE INVENTION

The present invention is directed to the mechanical power engineeringfor refrigeration and heat pumps.

BACKGROUND OF THE INVENTION

Refrigeration cycles transfer thermal energy from a region of lowtemperature to one of higher temperature, the reversed Carnot cycle isthe perfect model for the refrigeration cycle operating between twofixed temperatures, the most ideal cycle, which has the maximum thermalefficiency, maximum coefficient of performance, and serves as a standardagainst which actual refrigerator cycles can be compared, reversedCarnot cycle consist of 4 processes, 2 isentropic processes forexpansion and compression, and 2 isothermal processes for heat rejectionand heat absorption.

Now most of the refrigerators and heat pumps are working on theprinciple of the ideal Vapor compression cycle, that cycle was built onthe principals of the reversed Carnot cycle, but this cycle is deviatefrom the reversed Carnot for the following reasons:

-   -   1—The refrigerant shall enter the compressor at the vapor phase,        for the compressor operation.    -   2—Throttling valve is used in expansion process (constant        enthalpy process)    -   3—The heat rejection and absorption at a constant pressure        process, for more practicality.

SUMMARY OF INVENTION

The intent of this invention is to prove a new ideal refrigerator cycle(the Liquid compression cycle) which has a coefficient of performancehigher than the Vapor compression cycle.

Technical Problems

The coefficient of performance for the ideal Vapor compressionrefrigeration cycle (VCRC) is lower than the reversed Carnot cycle dueto the deviation of its ideal process from the reversed Carnot, thismeans that the ideal VCRC will consume more electric power than thereversed Carnot cycle at the same refrigeration capacity or when the twocycles are operating at the same maximum and minimum temperatures.

Moreover, all issues related to the compressors in the actual VCRC, forexample the maintenance, lubrication system, and it's high cost, etc.

Problems Solution

The liquid refrigerant pump in the liquid compression refrigerationcycle (LCRC) is acting the same function of the compressor in the VCRCto solve all the above problems.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 showing the LCRC on T-S and T-H diagram.

FIG. 2 showing the COP levels for Carnot, LCRC, and VCRC.

FIG. 3 showing the VCRC on T-S and T-H diagrams.

FIG. 4 showing a simple schematic diagram for the main components.

DETAILED DESCRIPTION

Liquid compression cycle (LCRC) is a cycles, that can be applied in therefrigeration and heat pumps applications, this cycle has achieved theperformance of the reversed Carnot cycle, unlike the vapor compressioncycle, where a clear deviation from the reversed Carnot cycle isappeared in it's ideal case, the deviation is occur due to thecompression process where the refrigerant has to be compressed to atemperature higher than the condensing temperature, and the constantenthalpy process in the expansion valve, where energy loss has occurreddue to the irreversibility of the process, these deviations from Carnotcycle have been solved in the Liquid Compression Cycle (LCRC) to achievea thermal efficiency more than the Vapor Compression Cycle (VCRC)efficiency, and we will prove that later.

Liquid compression cycle consists of 5 processes, 3 isentropicprocesses, one isothermal process, and one isobaric process, the cycle(T-H) and (T-S) diagrams are shown in FIG. 1.

Process (1-2) isentropic compression in a liquid pump

Process (2-3) isentropic expansion in a nozzle

Process (3-4) isothermal heat absorption in an evaporator

Process (4-5) isentropic compression in a diffuser

Process (5-1) isobaric heat rejection in a condenser

Liquid compression cycle is working between 3 levels of pressure, therefrigerant enter the pump at state 1 as a saturated liquid andcompressed from the condenser pressure to a higher level pressure, thenthe refrigerant enters the expansion nozzle to reach the evaporatorpressure, during this expansion process the refrigerant lose a lot ofinternal energy as well as the pressure is decreasing during theexpansion, these amount of energy is converted to kinetic energy atstate 3, then the refrigerant is absorbing heat during the isothermalprocess in the evaporator to reach state 4 in a 2 phase region, then thepressure is regained in the diffuser by converting a part of the kineticenergy again to enthalpy, the refrigerant is isentropic compressed tothe condenser pressure at state 5, then the heat is rejected to theambient at constant pressure to enter the pump again at state 1, FIG. 4is showing a schematic diagram for the cycle main components.

Example

The following example is showing how the Liquid compression cycle hasachieved the performance of the reversed Carnot cycle comparing with theVapor compression cycle at the same levels of condenser and evaporatorpressure.

As shown in FIG. 2 a comparison between Carnot, LCRC, and VCRC accordingto the COP levels

Assume refrigerant 134 a in the Liquid compression cycle is workingbetween the condenser pressure P₁=1.2 Mpa, and the evaporator pressureP₃=0.36 Mpa, with refrigerant effect 14 kJ/(kg of refrigerant), now, wecan describe and calculate the properties at each state.

-   -   @state 1: saturated liquid phase, P₁=1.2 Mpa, T₁=46° C., =117.77        kj/kg, s₁=0.424 kj/kg. K, v₁=0.00089 m3/kg.    -   @state 2: sub-cooled phase, P₂ shall be calculated by applying        the energy equation on the total cycle, as follows:

w _(p) =q _(co) −q _(ev)=(T ₁ −T ₃)Δs

And,

Δs=14/(5.8+273)=0.05 KJ/Kg

Hence,

w _(p)=(46−5.8)0.05=2.01 KJ/Kg

But,

w _(p) =v ₁(P ₂ −P ₁)

P ₂=(2.01/0.00089)+1200=3458 Kpa=3.46 Mpa

For isentropic compression, s ₂ =s ₁=0.424 KJ/Kg·K

And,

h ₂ =v ₁(P ₂ −P ₁)+h ₁=0.00089(3458−1200)+117.77=119.8 KJ/Kg

-   -   @state 3: P₃=0.36 Mpa, for isentropic expansion s₂=s₃=0.424        KJ/Kg·K, T₃=5.8° C., x₃=0.275,        h₃=h_(f)+x₃h_(fg)=59.72+(0.275×194.08)=113.1 kj/kg.    -   @state 4: P₄=P₃=0.36 Mpa, calculating s₄=Δs+s₃=0.424+0.05=0.474        kj/kg·K, x₄=0.347, calculating        h₄=h_(f)+x₄h_(fg)=59.72+(0.347×194.08)=127.04 kj/kg    -   @state 5: P₅=P₁=1.2 Mpa, for isentropic compression s₅=s₄=0.474        kj/kg·K, x₅=0.1015,        h₅=h_(f)+x₅h_(fg)=117.77+(0.102×156.1)=133.61 kj/kg    -   Assume that the ideal Vapor Compression cycle (VCRC) is working        at the same evaporator and condenser pressure as shown in FIG.        3:    -   @state 1: P₁=1.2 Mpa, h₁=117.77 kj/kg    -   @state 2: at throttling process, h₂=h₁=117.77 kj/kg    -   @state 3: P₃=0.36 Mpa, h₃=253.81 kj/kg, s₃=0.9283 kj/kg    -   @state 4: for isentropic compression s₄=s₃=0.928 kj/kg·K, T₄=50°        C., P₄=1.2 Mpa, h₄=278.27 kj/kg

A—the Coefficient of Performance (COP) for the Rev. Carnot, LCRC, andVCRC:

COP_(carnot) =T ₃/(T ₁ −T ₃)=278.8/(46−5.8)=7

COP_(LCC) =q _(ev) /w _(p)=14/2=7

COP_(VCC) =q _(ev) /w _(c)=(h ₃ −h ₂)/(h ₄ −h ₃)=136.04/24.46=5.56

B— Special Configuration of the Nozzle and Diffuser Devices for theLCRC:

In the theoretical study of the liquid compression cycle, specialconsiderations into nozzle and diffuser shall be considered:

i. Diffuser Inlet Velocities

Defining the relation between the inlet and outlet velocities byapplying the energy balancing equation on the diffuser,

h ₄+(V ₄ ²/2)=h ₅+(V ₅ ²/2),

(V ₄ ²/2)−(V ₅ ²/2)=Δh _(D)

Dividing the two terms by (V₄ ²/2)

$\begin{matrix}{{{1 - \frac{V_{5}^{2}}{V_{4}^{2}}} = \frac{2\Delta \; h_{D}}{V_{4}^{2}}}{\frac{V_{5}}{V_{4}} = \sqrt{1 - \frac{2\Delta \; h_{D}}{V_{4}^{2}}}}} & \left( {1a} \right)\end{matrix}$

Defining the relation between the inlet and outlet velocities byapplying the mass balancing equation on the diffuser,

$\begin{matrix}{{\frac{A_{5} \cdot V_{5}}{v_{5}} = \frac{A_{4} \cdot V_{4}}{v_{4}}}{\frac{V_{5}}{V_{4}} = {{\frac{v_{5}}{v_{4}} \cdot \frac{A_{4}}{A_{5}}} =}}} & \left( {2a} \right)\end{matrix}$

From equation (1a) and (2a)

$\begin{matrix}{{{\frac{v_{5}}{v_{4}} \cdot \frac{A_{4}}{A_{5}}} = \sqrt{1 - \frac{2\Delta \; h_{D}}{V_{4}^{2}}}}{{Then},}} & \; \\{V_{4} = \sqrt{\frac{2\Delta \; h_{D}}{1 - {\frac{v_{5}^{2}}{v_{4}^{2}} \cdot \frac{A_{4}^{2}}{A_{5}^{2}}}}}} & \left( {3a} \right)\end{matrix}$

By substituting in equation 3, where,

v₄=0.0202 m3/kg, and v₅=0.0025 m3/kg (From the previous example)

$V_{4} = \frac{\sqrt{2\Delta \; h_{D}}}{\sqrt{1 - {0.0153\frac{A_{4}^{2}}{A_{5}^{2}}}}}$

But from the above relation, we found that;

$\sqrt{1 - {0.0153\frac{A_{4}^{2}}{A_{5}^{2}}}} \approx 1$

Hence,

V ₄≈√{square root over (2Δh _(D))}  (4a)

ii. Nozzle Outlet Velocities

Defining the relation between the inlet and outlet velocities byapplying the energy balancing equation on the diffuser,

h ₂+(V ₂ ²/2)=h ₃+(V ₃ ²/2),

(V ₃ ²/2)−(V ₂ ²/2)=Δh _(N)

Dividing the two terms by (V₂ ²/2)

$\begin{matrix}{{{1 - \frac{V_{2}^{2}}{V_{3}^{2}}} = \frac{2\Delta \; h_{N}}{V_{3}^{2}}}{\frac{V_{2}}{V_{3}} = \sqrt{1 - \frac{2\Delta \; h_{N}}{V_{3}^{2}}}}} & \left( {1b} \right)\end{matrix}$

Defining the relation between the inlet and outlet velocities byapplying the mass balancing equation on the diffuser,

$\begin{matrix}{{\frac{A_{3} \cdot V_{3}}{v_{3}} = \frac{A_{2} \cdot V_{2}}{v_{2}}}{\frac{V_{2}}{V_{3}} = {\frac{v_{2}}{\; v_{3}} \cdot \frac{A_{3}}{A_{2}}}}} & \left( {2b} \right)\end{matrix}$

From equation (1b) and (2b)

$\begin{matrix}{{{\frac{v_{2}}{\; v_{3}} \cdot \frac{A_{3}}{A_{2}}} = \sqrt{1 - \frac{2\Delta \; h_{N}}{V_{3}^{2}}}}{{Then},}} & \; \\{V_{3} = \sqrt{\frac{2\Delta \; h_{D}}{1 - {\frac{v_{2}^{2}}{v_{3}^{2}} \cdot \frac{A_{3}^{2}}{A_{2}^{2}}}}}} & \left( {3b} \right)\end{matrix}$

By substituting in equation 3b,

Where,

v₃=0.016 m3/kg, and v₂=0.00089 m3/kg (From the previous example)

$V_{3} = \frac{\sqrt{2\Delta \; h_{N}}}{\sqrt{1 - {0.003\frac{A_{3}^{2}}{A_{2}^{2}}}}}$

From the above equation, we find that;

$\sqrt{1 - {0.003\frac{A_{3}^{2}}{A_{2}^{2}}}} \approx 1$

Hence,

V ₃≈√{square root over (2Δh _(N))}  (4b)

C— General Configuration on the Actual Liquid Compression Cycle:

-   -   1. As shown in the previous example the higher pressure level is        calculated according to the minimum potential work needed for        the reversible Liquid compression cycle, in the actual cycle,        that pressure shall be increased to overcome all        irreversibilities in the cycle.    -   2. The expansion process occur in the nozzle will be adiabatic        irreversible process, where;

$\begin{matrix}{\eta_{{is}.N} = \frac{\Delta \; h_{act}}{\Delta \; h_{is}}} \\{= {\left( {{Actual}\mspace{14mu} {Kinetic}\mspace{14mu} {energy}\mspace{14mu} {at}\mspace{14mu} {exit}} \right)\text{/}}} \\{\left( {{Isentropic}\mspace{14mu} {Kinetic}\mspace{14mu} {energy}\mspace{14mu} {at}\mspace{14mu} {exit}} \right)} \\{= \frac{V_{act}^{2}}{V_{is}^{2}}}\end{matrix}$

-   -   3. The compression process occur in the diffuser will be        adiabatic irreversible process, where;

$\begin{matrix}{\eta_{{is}.D} = \frac{\Delta \; h_{is}}{\Delta \; h_{act}}} \\{= {\left( {{Isentropic}\mspace{14mu} {Kinetic}\mspace{14mu} {energy}\mspace{14mu} {at}\mspace{14mu} {exit}} \right)\text{/}}} \\{\left( {{Actual}\mspace{14mu} {Kinetic}\mspace{14mu} {energy}\mspace{14mu} {at}\mspace{14mu} {exit}} \right)} \\{= \frac{V_{is}^{2}}{V_{act}^{2}}}\end{matrix}$

-   -   4. The compression process occur in the pump will be adiabatic        irreversible process.    -   5. A pressure drop shall occur in evaporator and condenser coil,        the same as the actual Vapor compression cycle.

Advantages of the Liquid Compression Cycle on the Vapor CompressionCycle:

-   -   1. The coefficient of performance of LCRC is higher than VCRC.    -   2. If the refrigerant leaving the condenser in the sub-cooled        region, or state 1 is fall in the sub-cooled region, the COP of        the LCRC will slightly raised above the reversed Carnot cycle,        the limitation for this raise depending on the minimum        temperature approach between the refrigerant and the ambient or        the cooling medium.    -   3. The work addition process is occur in the liquid phase, thus        the actual process will be close to the isentropic process,        unlike the VCRC, the work addition process in the superheat        region, where more irreversibility has occur in the actual        cycle.    -   4. The constant enthalpy process in the expansion valve for the        VCRC, increasing the irreversibility in the ideal VCRC cycle, as        well as, the actual cycle, where there no expansion valve        throttling process in the LCRC.    -   5. The low refrigerant velocity for the vapor line and condenser        coil, will decreasing the friction loss in pipes, and hence the        irreversibility (or energy loss) will decrease in LCRC comparing        with VCRC.    -   6. The lubrication system challenges in the VCRC are not exist        in the LCRC by separating the lubricant from the refrigerant        path.    -   7. The LCRC is more economic than VCRC in maintenance, by        replacing the compressor with pump for work addition process.    -   8. The initial cost of LCRC is lower than VCRC in the reason of        using pump instead of the compressor.

Disadvantages of the Liquid Compression Cycle on the Vapor CompressionCycle

-   -   1. The required refrigerant mass flow rate is much higher than        VCRC for the same evaporator capacity however this increasing in        mass flow rate will not affecting on the total volume of the        cycle, that because the density of the liquid stat is much        higher than density at vapor stat, so the volume of the pump        will not increasing as compressors at higher refrigerant mass        flow rate, in addition the decreasing in condenser and        evaporator effect (heat transfer in KW/Kg of refrigerant mass)        will balance the increasing in refrigerant mass flow rate in        LCRC, so the total surface area of the condenser and evaporator        in LCRC will be close to the VCRC for the same cycle capacity.    -   2. The high refrigerant velocity for the liquid line and        evaporator coil in the LCRC, will increasing the friction loss        in pipes, and hence the irreversibility (or energy loss) will        increased in LCRC comparing with VCRC, however this energy loss        is too low if compared with the VCRC energy loss as discussed        above.

General Recommendation on the Liquid Compression Cycle:

-   -   1. The positive displacement pump could be more suitable for the        higher compression ratio compared to the required mass flow        rate.    -   2. Installing a refrigerant distributor before the evaporator        and condenser coils to divide the mass flow rate on a multiple        paths, will increase the heat transfer area and decreasing the        refrigerant paths, also the nozzle could be a part of the pump        casing, or installed directly after the pump to insure that the        expansion is occurred suddenly after compression process.    -   3. For preventing cavitations at the centrifugal pump suction        line a pressurized tank shall installed at the pump suction,        also the tank for keeping the condenser, and the suction line at        a constant pressure.

LEGEND

-   LCRC Liquid Compression Refrigeration Cycle-   VCRC Vapor Compression Refrigeration Cycle-   T Temperature-   P Pressure-   H enthalpy per unit of refrigerant mass-   S entropy per unit of refrigerant mass-   w_(p) Mechanical pump work per unit of refrigerant mass-   w_(c) Mechanical compressor work per unit of refrigerant mass-   q_(co) Heat rejected from condenser per unit of refrigerant mass-   q_(ev) Heat absorbed to evaporator per unit of refrigerant mass-   COP Coefficient Of Performance-   X Mass quality, the ratio of the vapor mass to the total mass of the    mixture.-   Δh_(N) Total Enthalpy difference in the diversion-conversion nozzle    -   Δh_(N)=Δh_(N2)−Δh_(N1)-   Δh_(N1) Enthalpy difference in the diversion section of the    diversion-conversion nozzle-   Δh_(N2) Enthalpy difference in the conversion section of the    diversion-conversion nozzle-   Δh_(D) Total Enthalpy difference in the diversion-conversion    diffuser    -   Δh_(D)=Δh_(D1)−Δh_(D2)-   Δh_(D1) Enthalpy difference in the diversion section of the    diversion-conversion diffuser-   Δh_(D2) Enthalpy difference in the conversion section of the    diversion-conversion diffuser-   P Pump.-   N Nozzle.-   D Diffuser.-   CO Condenser coil.-   EV Evaporator coil.-   Δh_(act) Actual enthalpy difference-   Δh_(is) Isentropic enthalpy difference-   V_(act) ²/2 Actual Kinetic energy-   V_(is) ²/2 Isentropic Kinetic energy-   η_(is,N) Isentropic efficiency of the nozzle-   η_(is,D) Isentropic efficiency of the diffuser

What is claimed:
 1. The Liquid compression refrigeration cycle (LCRC).Liquid compression refrigeration cycle (LCRC) is a new operating theoryfor refrigeration and heat pump applications derived from the idea ofthe reversed Carnot cycle, the cycle is consisting of 5 processes, 3isentropic processes, one isothermal process, and one isobaric process,the cycle (T-H) and (T-S) diagrams are shown in FIG.
 1. Process (1-2)isentropic compression in a liquid pump Process (2-3) isentropicexpansion in a nozzle Process (3-4) isothermal heat absorption in anevaporator coil Process (4-5) isentropic compression in a diffuserProcess (5-1) isobaric heat rejection in a condenser coil
 2. LCRCcomponents a) Pump b) Nozzle c) Evaporator coil d) Diffuser e) Condensercoil
 3. LCRC theory of operation Liquid compression cycle is workingbetween 3 levels of pressure, the refrigerant enter the pump at state 1as a saturated liquid and compressed from the condenser pressure to ahigher level pressure, then the refrigerant enters the expansion nozzleto reach the evaporator pressure, during this expansion process therefrigerant lose a lot of internal energy as well as the pressure isdecreasing during the expansion, these amount of energy is converted tokinetic energy at state 3, then the refrigerant is absorbing heat duringthe isothermal process in the evaporator to reach state 4 in a 2 phaseregion, then the pressure is regained in the diffuser by converting apart of the kinetic energy again to enthalpy, the refrigerant isisentropic compressed to the condenser pressure at state 5, then theheat is rejected to the ambient at constant pressure to enter the pumpagain at state 1, FIG. 4 is showing a schematic diagram for the cyclemain components.
 4. (canceled)